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<h4>Lesson Narrative</h4>
<p>In earlier lessons, students factored the standard form of a quadratic function to find its solutions, or zeros.
Students will now be provided the zeros of a quadratic function and convert them into the factored form and standard
form of that function.</p>
<p>Students will also distinguish between finding a quadratic function that has certain zeros and finding the specific
quadratic function that has certain zeros and passes through a particular point. They will learn to differentiate
between these related quadratic functions.</p>
<h4>Learning Goals (Teacher Facing)</h4>
<ul class="os-raise-noindent">
<li> Convert fluently between a quadratic function's zeros, its factored form, and its standard form. </li>
<li> Identify the zeros on the graph of a quadratic function and use them to write the standard form of that function.
</li>
<li> Use the intercept form of a quadratic function, \(f(x) = a(x − p)(x − q)\), to define a specific
function given its zeros and a point. </li>
</ul>
<h4>Learning Targets (Student Facing) </h4>
<ul class="os-raise-noindent">
<li> Find the standard form of a quadratic function given its zeros. </li>
<li> Find the standard form of a quadratic function given its graph. </li>
<li> Use the intercept form of a quadratic function to define a specific function given its zeros and a point. </li>
</ul>
<table class="os-raise-textheavytable">
<caption>Texas Essential Knowledge and Skills (TEKS)</caption>
<thead>
<tr>
<th scope="col">TEKS
</th>
<th scope="col">
Explanation of Coverage
</th>
</tr>
</thead>
<tbody>
<tr>
<td>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</td>
<td>Math process coverage: Lesson provides content that supports this TEKS.
</td>
</tr>
<tr>
<td>
A6(C) write quadratic functions when given real solutions and graphs of their related equations.
</td>
<td>
<p>Full coverage: Lesson provides content that covers all parts of this TEKS.</p>
</td>
</tr>
</tbody>
</table>
<br>
<h4>Lesson Activities</h4>
<p>Here are the instructional activities for the lesson:</p>
<ul class="os-raise-noindent">
<li> 8.11.1: Relating a Quadratic Function and Its Zeros </li>
<li> 8.11.2: Finding a Quadratic Function from Its Zeros </li>
<ul>
<li> 8.11.2: Self Check </li>
<li> 8.11.2: Additional Resources </li>
</ul>
<li> 8.11.3: Finding a Quadratic Function from Its Zeros and a Point </li>
<ul>
<li> 8.11.3: Self Check </li>
<li> 8.11.3: Additional Resources </li>
</ul>
<li> 8.11.4: Writing Quadratics When Given Any Format </li>
</ul>
<p>Students will also complete a series of problems in the 8.11.5: Practice.</p>
<h4>Required Materials</h4>
<ul class="os-raise-noindent">
<li> Paper and pencil </li>
<li> Graphing technology </li>
</ul>
<h4>Required Preparation</h4>
<ul class="os-raise-noindent">
<li> Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student
has their own device. </li>
</ul>
<h4>Lesson Vocabulary</h4>
<p>During this lesson, it is important to:</p>
<ul class="os-raise-noindent">
<li> Familiarize students with the vocabulary words they will see throughout the lesson. </li>
<li> Encourage students to look for these words and notice their use and meanings. </li>
<li> Encourage students to use key vocabulary words in “math talk” and their written and oral
explanations. </li>
<li> Utilize a word wall. Sample cards are located here: <a
href="https://k12.openstax.org/contents/raise/resources/8ed3aa68763498713b44d3c2e537ffe61b4755f0"
target="_blank">Mathematics Vocabulary Word Wall Cards</a>. </li>
</ul>
<p>Vocabulary words that are emphasized in this lesson:</p>
<table class="os-raise-textheavytable">
<thead>
<tr>
<th scope="col">
Previous Vocabulary
</th>
<th scope="col">
New Vocabulary
</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<ul>
<li> quadratic equation </li>
<li> quadratic function </li>
<li> factored form (of a quadratic expression) </li>
<li> standard form (of a quadratic expression) </li>
<li> variable </li>
<li> zero of the function </li>
</ul>
</td>
<td>
<ul>
<li> none </li>
</ul>
</td>
</tr>
</tbody>
</table>
<br>
<p>To support newcomers or students identified at the beginning level of language proficiency, share the following Quizlet links to help students gain an understanding of the academic vocabulary. Use the Spanish versions to anchor student understanding before bridging to the English versions. </p>
<ul>
<li><a href="https://quizlet.com/881785079/raise-unit-8-spn-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 8 Spanish Vocabulary</a></li>
<li><a href="https://quizlet.com/881565975/raise-unit-8-vocabulary-flash-cards/?i=5eauv9&x=1jqt" target="_blank">Unit 8 Vocabulary</a></li>
</ul>
<h4>Support for English Language Learners</h4>
<p>Throughout this lesson, activities are incorporated that align to the following ELPS. The suggested activities
are only a sampling of the types of support and scaffolding that can extend the learning for English language
learners. Continue to find additional opportunities as you build your own set of ELL learning routines.</p>
<ul>
<li>
ELPS 2(F) listen to and derive meaning from a variety of media such as audiotape, video, DVD, and CD-ROM to build
and reinforce concept and language attainment
</li>
<li>ELPS 3(E) share information in cooperative learning interactions </li>
<li>ELPS 3(F) ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete
vocabulary, including key words and expressions needed for basic communication in academic and social contexts,
to using abstract and content-based vocabulary during extended speaking assignments </li>
</ul>
<br>
<h4>Support for Building Character</h4>
<p>Throughout this unit, find ways to encourage and support students to work on cultivating their
<strong>curiosity</strong>.</p>
<p>Here are some tips to try during this lesson:</p>
<ul class="os-raise-noindent">
<li> <a href="https://characterlab.org/tips-of-the-week/the-power-of-questions/" target="_blank">The Power of
Questions</a> </li>
<li> <a href="https://characterlab.org/tips-of-the-week/throughlines/" target="_blank">Throughlines</a> </li>
</ul>
<p>You can find other tips located here in the <a href="https://characterlab.org/playbooks/curiosity/"
target="_blank">Playbook on Curiosity</a> from Character Lab.</p>